This disclosure relates to methods for measuring river discharge and, more particularly, to a method for measuring river discharge in the presence of moving sediment that can cause bottom-tracking data to become biased.
Acoustic Doppler flow measurement systems remotely measure vertical profiles of water flow velocity, earth-referenced platform velocity, and water depth. These three parameters are measured substantially continuously as the platform carrying the measurement equipment travels across a channel. Water velocity is determined throughout a vertical water column by measuring the Doppler shifted echoes from small particles. The platform's velocity has been determined by measuring the Doppler shifted echoes from the channel bottom or by using electromagnetic navigation systems such as GPS. Channel flow velocity is computed at incremental positions (“stations”) across the channel by subtracting the platform referenced channel flow velocity profile measurements from the earth-referenced platform velocity measurements. River cross section is determined from the water depth and platform position measurements. Channel discharge is then computed from the product of the measured mean flow velocity and the channel cross-sectional area. One such method is disclosed in U.S. Pat. No. 6,714,482. In order to determine the current flow rate, it is necessary to correct the measured current for the earth-referenced platform velocity that is determined from the Doppler-shifted echoes from the channel bottom. If the channel bottom is moving, the acoustic measurements become biased and the platform velocity cannot be accurately measured this way.
The algorithm of discharge measurement was originally developed by Christensen and Herrick (1982) “Mississippi River test: Volume 1: Final report” DCP4400/300, prepared for the U.S. Geological Survey by AMETEK/Straza Division, El Cajon, Calif., under contract No. 14-08-0001-19003, and Simpson and Oltmann (1993) “Discharge-Measurement system using an acoustic Doppler current profiler with application to large rivers and estuaries. United States Geological Survey, Water-Supply Paper 2395, where normal component of the measured water velocity across the river is combined with the cross-sectional area to calculate the total discharge.
The general equation for determining river discharge is written as follows:
                    Q        =                  ∫                                    ∫              S                        ⁢                                          u                ·                ξ                            ⁢                              ⅆ                s                                                                        (        1        )            where Q is the discharge, S is the cross-section area along a boat's track, u is the water velocity vector, and ξ is the unit vector normal to the boat's track at a differential area ds. The area increment ds is determined by the following:ds=|Ub|dzdt  (2)where dz is the depth increment, dt is the time increment, |Ub| is the boat speed determined as |Ub|=√{square root over (Ubx2+Uby2)}. The coordinate system is defined as follows: z is the vertical axis (FIG. 1), z=0 is the river bottom, and z=H is the water surface, (x, y) form a right hand Cartesian coordinate system with the positive x pointing downstream (FIG. 2).Eq. (1) can be rewritten using the cross-product of the velocity vector at a depth cell and the boat velocity vector:
                    Q        =                                            ∫              0              t                        ⁢                                                            [                                                            ∫                      0                      II                                        ⁢                                          u                      ⁢                                                                                          ⁢                                              ⅆ                        z                                                                              ]                                ·                ξ                            ⁢                                                                U                  b                                                            ⁢                                                          ⁢                              ⅆ                t                                              =                                    ∫              0              T                        ⁢                                          ∫                0                II                            ⁢                                                                    (                                          u                      ×                                              U                        b                                                              )                                    ·                  k                                ⁢                                                                  ⁢                                  ⅆ                  z                                ⁢                                                                  ⁢                                  ⅆ                  t                                                                                        (        3        )            where T is the total transect time, and k is the unit vector in the vertical direction. In practice, the discharge integral is approximated by the following summation:
                    Q        =                  Δ          ⁢                                          ⁢          t          ⁢                                    ∑                              i                =                1                            M                        ⁢                                                  ⁢                                                            [                                                            (                                                                                                    U                            _                                                    w                                                ×                                                  U                          b                                                                    )                                        ·                    k                                    ]                                i                            ⁢                              H                i                                                                        (        4        )            where Hi is the average water depth of a measurement segment i, Δt is the averaging interval for the segments, M is the total number of the segments in the transect, N is the total number of the good depth cells, Ūw is the depth averaged water velocity. The summation is performed over a two dimensional grid in the (Y-Z) plane.
The SonTek RiverSurveyor (RS) is an acoustic Doppler system that measures river discharge from a boat. By measuring water and boat velocities and water depth along the boat's track, RiverSurveyor calculates river discharge as the boat moves from one side of the river to the other side. Mounted on a boat, the ADP measures the water velocity relative to the boat while the GPS provides the boat velocity. The absolute water velocity is obtained by subtracting the boat velocity Ub from the measured velocity Um as:Uw=Um−Ub  (5)
These are combined with the depth and distance measurements to compute discharge according to Eq 4.
Traditionally, two complementary methods have been in use for measuring river discharge. One method, called the “section-by-section” or “stationary” method, was established by ISO/USGS. It involves making a series of measurements (generally 20-25) at locations (commonly referred to as stations) along a straight line transecting from one side of the river to the other. Typically, a graduated tag-line is strung from one side of the river to the other side, to indicate the direction of the traverse and to mark the location of measurement stations. Measurements of depth, water velocity and distance along the transect are made at each individual station. Water velocity data are averaged over a time interval that is long enough to reduce natural flow variations. Ideally, the velocity measurement device is kept as still as possible during this averaging time. Depth is measured using separate means that include wading/depth sounding rods, echosounder, etc. This method has also been adopted for use from structures such as cableways and causeways where a velocity measurement device is lowered into water that was otherwise too deep or hazardous for wading measurements.
Another technique of discharge monitoring involves the use of a moving platform (boat) that traverses the width of the river while continuously measuring the water velocity profile, depth, and distance traveled. The distance traveled is measured using a high accuracy Differential GPS (DGPS) receiver and/or an acoustic speed over ground (SOG) device more commonly known as bottom-tracking. In principle, the GPS and SOG data can be combined via a Kalman filter to produce a more robust estimate of the boat speed. Brumley B., Cabrera R., Deines K., Terray E. (1991) Performance of a broad-band acoustic Doppler current profiler. IEEE Journal of Oceanic Engineering 16:402-407. Although this augmentation method generally produces more accurate positioning it does not improve performance in the presence of a moving bottom. Moving bed conditions occur when the river bottom becomes liquefied (typically in high sediment or flood conditions), or when a fluid layer of mud covers the river bottom. To improve bottom tracking performance in the presence of a moving bottom, lower frequency acoustic devices have been traditionally employed in order to increase bottom penetration. However, lower frequency systems have generally lower precision and resolution and are more expensive, bulkier, and harder to handle.
The use of DGPS has certain limitations including: a high initial upfront expense for the unit and ongoing costs; poor coverage away from the coastal beacons due to terrain; and low availability of the correction broadcasts internationally. It is not available in many developing countries or in deep canyons and in locations remote from reference stations where flow discharge measurements are often desired. Additionally, DGPS hardware is often expensive and even high quality commercial DGPS receivers do not always perform adequately in small rivers and canals.
Recently, the stationary method of discharge measurement has been adapted to be used from a floating platform (boat) thereby removing the depth limitation of wading measurements. In this method, the river is transected in a set of increments or ‘stations’. In this case, the platform transporting the current-measuring device is held as stationary as possible at each station so as to minimize the platform speed relative to the ground so that the speed over ground does not need to be measured. This technique generally requires that the platform position be within about 0.5 to 1.0 m of each station during each measurement. In one example of this operation, at each station, the current profile measurements are typically averaged for a period of approximately one 40 to 60 second measurement interval (MI) to improve precision of Doppler current profiling data and reduce effects of natural flow variability. The main difference with the continuous measurement method is that at each station the boat is kept relatively stationary (by some means such as anchor or speed control) and hence the boat speed over ground does not need to be measured accurately on a second by second basis. As a common practice, all of the stations lie in the same line so they all have a common azimuth, which is a fairly demanding requirement for a wider river and in the presence of ship traffic.
The latter section-by-section method offers improved performance in most extreme flow conditions: e.g., very low flows (Uw<0.1 nm/s) and very high flows (Uw>2 m/s). In this case, however, the accurate measurement of the platform's velocity in all conditions becomes more difficult, as there is no tagline to assist in station keeping. Therefore, there is a need to be able to obtain accurate velocity estimates of the floating platform in order to produce accurate discharge measurements in rivers of various widths, shipping traffic, and in a variety of flow regimes including floods when moving bottom conditions are likely to occur.